Discrete Dynamics in Nature and Society

Volume 2017 (2017), Article ID 8523495, 9 pages

https://doi.org/10.1155/2017/8523495

## Learning to Detect Traffic Incidents from Data Based on Tree Augmented Naive Bayesian Classifiers

^{1}Jiangsu Key Laboratory of Urban ITS, School of Transportation, Southeast University, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic, Sipailou No. 2, Xuanwu District, Nanjing 210096, China^{2}Huaiyin Institute of Technology, Key Laboratory for Traffic and Transportation Security of Jiangsu Province, Meicheng Rd, Huaian 223003, China

Correspondence should be addressed to Dawei Li

Received 25 April 2017; Revised 17 July 2017; Accepted 27 July 2017; Published 2 October 2017

Academic Editor: Gabriella Bretti

Copyright © 2017 Dawei Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study develops a tree augmented naive Bayesian (TAN) classifier based incident detection algorithm. Compared with the Bayesian networks based detection algorithms developed in the previous studies, this algorithm has less dependency on experts’ knowledge. The structure of TAN classifier for incident detection is learned from data. The discretization of continuous attributes is processed using an entropy-based method automatically. A simulation dataset on the section of the Ayer Rajah Expressway (AYE) in Singapore is used to demonstrate the development of proposed algorithm, including wavelet denoising, normalization, entropy-based discretization, and structure learning. The performance of TAN based algorithm is evaluated compared with the previous developed Bayesian network (BN) based and multilayer feed forward (MLF) neural networks based algorithms with the same AYE data. The experiment results show that the TAN based algorithms perform better than the BN classifiers and have a similar performance to the MLF based algorithm. However, TAN based algorithm would have wider vista of applications because the theory of TAN classifiers is much less complicated than MLF. It should be found from the experiment that the TAN classifier based algorithm has a significant superiority over the speed of model training and calibration compared with MLF.

#### 1. Introduction

Traffic congestion is a challenging problem in most of the big cities all over the world. Congestion leads to increasing traffic delays, higher fuel consumption, and negative environmental effects. The cost of total delay caused by traffic congestion in rural and urban areas is estimated to be around $1 trillion per year in the United States [1]. Traffic congestion can be classified into two categories: recurrent congestion generated by excess demand and unrecurrent congestion caused by incidents. Some studies have estimated that around 60% of all traffic congestion on highways is caused by incidents [2]. Due to the large losses caused by unrecurrent congestion, incident manage system (IMS) has been a key component of the advanced traffic management system now.

As a core technique in IMS, automatic incident detection (AID) algorithms have also become an interesting and active research topic. A considerable amount of research has addressed this problem and several techniques have been developed over the last few decades. Depending on the methodology, an algorithm is usually classified into one of five major categories: comparative algorithms, statistical algorithms, time-series and filtering based algorithms, traffic theory based algorithms, and advanced algorithms.

The California algorithms are classic examples of the comparative algorithms, which are one of the first widely implemented incident detection algorithms developed [3]. They are usually used as benchmarks for evaluating the performance of other algorithms. Examples of the statistical algorithms include the standard normal deviate (SND) algorithm [4] and the Bayesian Algorithms [5], which use standard statistical techniques to identify sudden changes in the traffic flow parameters. Time-series and filtering algorithms treat the traffic flow parameters as time-series. The deviation from the modeled time-series behavior is used for indication of incidents. The moving average (MA) algorithm [6] and the exponential smoothing based algorithms [7] are included in this category. One classic example of traffic theory based algorithms is McMaster algorithm, which is based on the catastrophe theory. McMaster algorithm determines the state of traffic based on its position in the flow-density plot and detects incidents based on the transition of the point from one state to another [8]. In order to improve the detection performance, the latest trend has been the development of advanced algorithms, which are based on advanced mathematical formulation. Neural Networks based algorithms [9, 10], which have an attractive performance in the lab environment, are classified into this category.

By reviewing the existing incident detection algorithms, it should be noted that most of these algorithms, which perform well in the lab environment, have not been used in practice. The biggest reason is that, it is usually difficult to transfer these algorithms from site to site and keep a well performance. To meet the universality requirements for which the advanced traffic management systems called, the Bayesian networks have been used to develop universal algorithms [11, 12]. According to the testing results, these algorithms demonstrate very stable performance and strong transferability. However, in the previous studies, the Bayesian networks based algorithms strongly depend on the knowledge of experts. For instance, the determination of the Bayesian network structure and the discretization of continuous attributes are both artificially predetermined in these studies.

As a special case of Bayesian network, the naive Bayesian classifier does not need the predetermination of network structure [13]. However, the naive Bayesian classifier has too strict assumptions on the independent relations of variables. To improve the performances, many improved naive Bayes algorithms are proposed in literature, such as the Averaged One-Dependence Estimators (AODE) [14], Weighted Average of One-Dependence Estimators (WAODE) [15], Hidden Naive Bayes (HNB) [16], Deep Feature Weighted Naive Bayes (DFWNB) [17], Discriminatively Weighted Naive Bayes (DWNB) [18], Averaged Tree Augmented Naive Bayes (ATAN) [19], and Super Parent TAN (SP) [14].

In this study, in order to reduce the dependency on experts’ knowledge, a tree augmented naive Bayesian (TAN) classifier, which is a special form of Bayesian networks, is chosen to develop an incident detection algorithm in this paper. The TAN classifier can reduce the dependency on experts’ knowledge, because the structure and parameters of the proposed TAN classifier are both learned from the data, and an entropy-based method is proposed for the discretization of continuous variables completely depending on the data. The performance of this algorithm would also be evaluated using a simulation dataset.

The remaining part of the article is structured as follows: Section 2 is a simple introduction of TAN classifier. Section 3 presents the procedure of data preprocessing. Section 4 discusses the development and implementation of the TAN classifier for incident detection. In Section 5, an experiment of this algorithm with a simulation dataset is carried out. Finally, Section 6 gives some conclusions and remarks.

#### 2. TAN Classifier

##### 2.1. Bayesian Networks

Since TAN classifier is a special case of Bayesian networks, it is necessary to introduce Bayesian networks first. Bayesian networks are directed acyclic graphs that allow efficient and effective representation of the joint probability distribution over a set of random variables [20]. Formally, a Bayesian network for a set of random variables is a pair . The first component, , is a directed acyclic graph whose vertices correspond to the random variables , and whose edges represent direct dependencies between the variables. The graph , which is also called the structure of this Bayesian network, encodes independence assumption: each variable is independent of its no-descendants given its parents in . The second component of the pair represents the set of parameters that quantifies the network. It contains a parameter for each possible value of , and of , where denotes the set of parents of in . A Bayesian network defines a unique joint probability distribution over given by

If a Bayesian network is used for incident detection, it must contain a class variable INC and attribute variables . means an incident has happened. denote traffic flow parameters. When it is implemented in IMS, are input in real time, and this Bayesian network is used to update the post probability .

Because of the independence assumption, in a Bayesian network for incident detection, the class variable INC must get links to all the attribute variables; therefore each and every piece of information about attribute variables can be made use of to update the incident probability. Therefore, the structure of this Bayesian network cannot be learned using any unrestricted learning algorithms. In the previous studies, it is manually determined according to experts knowledge. Figure 1(a) presents a possible structure of the Bayesian networks for incident detection.